where \(Y_i\)  set of all pixel in the generated map, 1 0 .3 1\(\mathbb {Y}_i^+\) represents the top \(n\%\)  pixels within the bounding box selected through multinomial sampling and 1 0 .3 1\(\mathbb {Y}_i^-\) represents top \(-n\%\)  pixels anywhere that are derived using uniform sampling from the activations of whole image sorted in reverse order. These pixels are derived from unreliable attention maps and may contain incorrect labels. To deal with this uncertainty, we select only a few (see experimental details for exact values) pixels from the foreground and background while rejecting others [1]}, [2]}. Therefore, the final set of foreground and background pixels for calculating loss are:
\(\varphi (\mbox{\sbox {}{$\mathbb {Y}$}\hspace{0.0pt}{1 0 .3 1}\unknown. {\usebox {}}}_i^{+,-}) = \varphi (\mbox{\sbox {}{$\mathbb {Y}_i^+$}\hspace{0.0pt}{1 0 .3 1}\unknown. {\usebox {}}})\cup \varphi (\mbox{\sbox {}{$\mathbb {Y}_i^-$}\hspace{0.0pt}{1 0 .3 1}\unknown. {\usebox {}}})\) 
